[{"year":"2007","department":[{"_id":"10020"}],"page":"239-242","article_type":"original","citation":{"dgps":"Ahlswede, R. (2007). The final form of Tao's inequality relating conditional expectation and conditional mutual information. *ADVANCES IN MATHEMATICS OF COMMUNICATIONS*, *1*(2), 239-242. AMER INST MATHEMATICAL SCIENCES. doi:10.3934/amc.2007.1.239.

","apa_indent":"Ahlswede, R. (2007). The final form of Tao's inequality relating conditional expectation and conditional mutual information. *ADVANCES IN MATHEMATICS OF COMMUNICATIONS*, *1*(2), 239-242. doi:10.3934/amc.2007.1.239

","harvard1":"Ahlswede, R., 2007. The final form of Tao's inequality relating conditional expectation and conditional mutual information. *ADVANCES IN MATHEMATICS OF COMMUNICATIONS*, 1(2), p 239-242.","bio1":"Ahlswede R (2007)

The final form of Tao's inequality relating conditional expectation and conditional mutual information.

ADVANCES IN MATHEMATICS OF COMMUNICATIONS 1(2): 239-242.","angewandte-chemie":"R. Ahlswede, “The final form of Tao's inequality relating conditional expectation and conditional mutual information”, *ADVANCES IN MATHEMATICS OF COMMUNICATIONS*, **2007**, *1*, 239-242.","ieee":" R. Ahlswede, “The final form of Tao's inequality relating conditional expectation and conditional mutual information”, *ADVANCES IN MATHEMATICS OF COMMUNICATIONS*, vol. 1, 2007, pp. 239-242.","default":"Ahlswede R (2007)

*ADVANCES IN MATHEMATICS OF COMMUNICATIONS* 1(2): 239-242.","lncs":" Ahlswede, R.: The final form of Tao's inequality relating conditional expectation and conditional mutual information. ADVANCES IN MATHEMATICS OF COMMUNICATIONS. 1, 239-242 (2007).","ama":"Ahlswede R. The final form of Tao's inequality relating conditional expectation and conditional mutual information. *ADVANCES IN MATHEMATICS OF COMMUNICATIONS*. 2007;1(2):239-242.","apa":"Ahlswede, R. (2007). The final form of Tao's inequality relating conditional expectation and conditional mutual information. *ADVANCES IN MATHEMATICS OF COMMUNICATIONS*, *1*(2), 239-242. doi:10.3934/amc.2007.1.239","mla":"Ahlswede, Rudolf. “The final form of Tao's inequality relating conditional expectation and conditional mutual information”. *ADVANCES IN MATHEMATICS OF COMMUNICATIONS* 1.2 (2007): 239-242.","chicago":"Ahlswede, Rudolf. 2007. “The final form of Tao's inequality relating conditional expectation and conditional mutual information”. *ADVANCES IN MATHEMATICS OF COMMUNICATIONS* 1 (2): 239-242.

","wels":"Ahlswede, R. (2007): The final form of Tao's inequality relating conditional expectation and conditional mutual information *ADVANCES IN MATHEMATICS OF COMMUNICATIONS*,1:(2): 239-242.","frontiers":"Ahlswede, R. (2007). The final form of Tao's inequality relating conditional expectation and conditional mutual information. *ADVANCES IN MATHEMATICS OF COMMUNICATIONS* 1, 239-242."},"date_created":"2010-04-28T11:50:16Z","title":"The final form of Tao's inequality relating conditional expectation and conditional mutual information","language":[{"iso":"eng"}],"_id":"1592060","status":"public","publisher":"AMER INST MATHEMATICAL SCIENCES","abstract":[{"text":"Recently Terence Tao approached Szemeredi's Regularity Lemma from the perspectives of Probability Theory and Information Theory instead of Graph Theory and found a stronger variant of this lemma, which involves a new parameter. To pass from an entropy formulation to an expectation formulation he found the following: Let Y, and X, X' be discrete random variables taking values in Y and X, respectively, where Y subset of [-1, 1], and with X' = f(X) for a (deterministic) function f. Then we have E(vertical bar E(Y vertical bar X') - E(Y vertical bar X)vertical bar) <= 2I(X Lambda Y vertical bar X')1/2. We show that the constant 2 can be improved to (2ln2)1/2 and that this is the best possible constant.","lang":"eng"}],"publication_status":"published","type":"journal_article","user_id":"67994","volume":1,"publication_identifier":{"issn":["1930-5346"]},"author":[{"full_name":"Ahlswede, Rudolf","id":"10479","last_name":"Ahlswede","first_name":"Rudolf"}],"keyword":["arithmetic progressions","information theoretic methods for combinators and number theory","Pinsker inequality","regularity lemma"],"date_updated":"2019-04-30T14:25:05Z","publication":"ADVANCES IN MATHEMATICS OF COMMUNICATIONS","external_id":{"isi":["000254707400004"]},"doi":"10.3934/amc.2007.1.239","intvolume":" 1","issue":"2","quality_controlled":"1","isi":1}]